While parents do, of course, have a huge impact on their children, I think it's overly simplistic to lay the ultimate responsibility at their feet. As raganwald points out (in the other direction), when there are feedback loops at play, the system can re-enforce other traits than you might hope for. Parents with no education in nutrition or no real supermarkets in their neighborhood can't be expected to feed their children well. A father in prison will have highly limited influence on his children. A teenage girl with limited access to contraceptives or abortion (or sex education) may end up a mother well before she's financially, emotionally, or intellectually prepared to perform that job well. Low-income, blue-collar communities may have perverse incentives to tie their children to their existing social and economic status, and resent and resist "modern society" in it's various guises.
Which is to say, I don't think you can approach this from a purely reductionist viewpoint. Yes, a given institution is limited to a degree by its inputs, but it's also the case that each component has the potential to make improvements, even if marginal.
I didn't mean to say only one is responsible; this is in the context of raganwald's essay about how quality meritocracies (presumably not needing much improvement) don't choose the best because they only maximize their inputs and don't necessarily work with all of those with the most potential. So I wrote about improving the inputs by examining the prior systems.
What I completely missed, and what you alluded to by mentioning people in prison, with bad parents, and so on, is that the present generation of families also have inputs -- the systems that they went through (education, military, commerce, etc.) and their own parents. The issues we have today are partly the results of mistakes made by parents living a hundred, five hundred, even a thousand years ago.
It's a depressing thought when expressed that way, but on the bright side, if we do as well as we can given our limited inputs today, we at least give the next generation of parents, teachers and employers a chance to do better than we could possibly have done.
Which is to say, I don't think you can approach this from a purely reductionist viewpoint. Yes, a given institution is limited to a degree by its inputs, but it's also the case that each component has the potential to make improvements, even if marginal.